(Adds White House comment, paragraph 12)

WASHINGTON, Jan 10 (Reuters) - Senate Majority Leader Harry Reid on Thursday urged President George W. Bush to consider cutting aid to Pakistan unless it restores full civil rights and does more to fight terrorism.

Reid, a Nevada Democrat, told Bush in a letter the assassination of opposition leader Benazir Bhutto two weeks ago had deepened worries about Pakistan's future and President Pervez Musharraf's "dismal record of performance."

"The record is so disturbing and the implications for our security so great that I believe additional pressure on President Musharraf to take the right steps is warranted," Reid wrote.

"His failure to do so should be met with real and significant consequences, including consideration of a cutoff of non-development funding," he added.

Reid, who called for a full review of U.S. policy after Musharraf imposed emergency rule in November, said Bush should make future aid conditional on removing limits on civil rights that remain in effect despite the formal end to the crackdown in mid-December.

Reid demanded that Musharraf restore freedom of the press and of association, free all political prisoners jailed during the crackdown, reinstate all of Pakistan's Supreme Court justices who were dismissed in November and support a United Nations investigation into Bhutto's death.

Musharraf has blamed al Qaeda for the gun-and-bomb attack that killed Bhutto, but many Pakistanis suspect that other enemies were involved. She died campaigning for a Jan. 8 election that has since been rescheduled to Feb. 18.

The crackdown prompted the U.S. Congress to place some democracy and anti-terrorism conditions on the U.S. multibillion dollar aid program to Pakistan, which borders troubled Afghanistan and which Washington sees as a key ally against Islamic extremism.

Budget legislation withheld $50 million of $300 million in military aid for Pakistan until Secretary of State Condoleezza Rice reports to Congress that Islamabad has restored democratic rights and an independent judiciary and was making concerted efforts to fight al Qaeda and Taliban militants.

U.S. lawmakers also limited use of the remaining $250 million in military aid to counterterrorism or law enforcement activities against al Qaeda and the Taliban.

A Senate aide said Reid's statement, which followed a similar warning to Bush in December from House of Representatives Speaker Nancy Pelosi, aimed to narrow Rice's leeway in declaring Pakistan has made progress, by tightening certification requirements.

White House National Security Council spokeswoman Kate Starr, asked about Reid's message, reiterated Bush's view that Pakistan "continues to be an important ally in the war on terror" and said Washington welcomed mext month's elections. (Reporting by Paul Eckert, Richard Cowan, Caren Bohan and Susan Cornwell, editing by Alan Elsner)

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